As you'll see this is a standard trig integral, but it's better to do it by trig substitution.

Construct a right triangle with a vertical leg of u, a horizontal leg of 1 and by Pythagoras the hypotenuse is . Let theta be the angle such that . You will also notice that , which makes an easy substitution. Make sure to calculate in terms of u, then make the full substitution, integrate, then back substitute.